Although every connected graph has a spanning tree, the same is not true for hypergraphs: consider the hypergraph on 4 vertices with all possible edges of size 3. You need to pick at least two edges but any 2 edges form a cycle.

On the other hand, if you make the number of hyperedges increase, eventually you get a spanning tree (in particular, in the complete hypergraph you always have a spanning tree).

So, what is the maximum number of hyperedges on a hypergraph without a spanning tree? I think $2^{|V|-1}$ is a lower bound, since you can do something similar to the example on 4 vertices. For that, take every edge on at least $\big\lceil\frac{|V|}{2}\big\rceil + 1$ vertices, in order to ensure that every pair of edges has intersection of size at least two. Another way of getting this is taking all possible edges on all but one vertex, but in this case the hypergraph is not connected.